smc-978-30-Area

Trigonometry, 2ADV T1 2020 HSC 22

The diagram shows a regular decagon (ten-sided shape with all sides equal and all interior angles equal). The decagon has centre .

The perimeter of the shape is 80 cm.

By considering triangle , calculate the area of the ten-sided shape. Give your answer in square centimetres correct to one decimal place. (4 marks)

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Trigonometry, 2ADV T1 2017 HSC 11e

In the diagram, is a sector of the circle with centre and radius 6 cm, where .

Find the exact value of the area of the triangle . (1 mark)

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Find the exact value of the area of the shaded segment. (1 mark)

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ii.

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Trigonometry, 2ADV T1 2007 HSC 4c

An advertising logo is formed from two circles, which intersect as shown in the diagram.

The circles intersect at and and have centres at and .

The radius of the circle centred at is 1 metre and the radius of the circle centred at is metres. The length of is 2 metres.

Use Pythagoras’ theorem to show that . (1 mark)

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Find and . (2 marks)

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Find the area of the quadrilateral . (1 mark)

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Find the area of the major sector . (1 mark)

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Find the total area of the logo (the sum of all the shaded areas). (2 marks)

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ii.

iii.

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iv.

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Trigonometry, 2ADV T1 2006 HSC 4a

In the diagram, represents a garden. The sector has centre and

The points and lie on a straight line and metres.

Copy or trace the diagram into your writing booklet.

Show that (1 mark)

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Find the length of . (2 marks)

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Find the area of the garden . (2 marks)

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ii.

iii.


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Trigonometry, 2ADV T1 2010 HSC 6b

The diagram shows a circle with centre and radius 5 cm.

The length of the arc is 9 cm. Lines drawn perpendicular to and at and respectively meet at .

Find in radians. (1 mark)

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Prove that is congruent to . (2 marks)

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Find the area of the shaded region. (2 marks)

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i.

ii.

MARKER’S COMMENT: Know the difference between the congruency proof of

and

. Incorrect identification will lose a mark.

iii.

♦♦ Mean mark below 30%.
MARKER’S COMMENT: Many students struggled to work in radians. Make sure you understand this concept.

iv.

♦ Mean mark 35%.





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